Incorporating limit notation

We're still going to keep our focus on polynomials for the moment, but now we want to describe those polynomials using limit notation. Using limits to describe the behavior of a polynomial near a constant is never very interesting because for all polynomials and all real numbers , it is always the case that .

First, describe in words what it means to say that .

What property do polynomials possess that makes it safe to say that for all polynomials ?

What is ?

If is a polynomial, which of the following is equal to ?

Check all that apply
We can also use limit notation--specifically, limits at infinity--to describe a function's end behavior. Enter a polynomial function such that and .

If is a polynomial and , what can you say about ?

Give an example of such a polynomial below.